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arXiv · 1709.01567

Vaisman solvmanifolds and relations with other geometric structures

Adrián Andrada·Marcos Origlia
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Abstract

We characterize unimodular solvable Lie algebras with Vaisman structures in terms of Kähler flat Lie algebras equipped with a suitable derivation. Using this characterization we obtain algebraic restrictions for the existence of Vaisman structures and we establish some relations with other geometric notions, such as Sasakian, coKähler and left-symmetric algebra structures. Applying these results we construct families of Lie algebras and Lie groups admitting a Vaisman structure and we show the existence of lattices in some of these families, obtaining in this way many examples of new solvmanifolds equipped with invariant Vaisman structures.

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Adrián Andrada, Marcos Origlia. 2020-04-02. Vaisman solvmanifolds and relations with other geometric structures. https://arxiv.org/abs/1709.01567

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